We recall a construction first proposed by
[1]}.
We can build a constrained maximum likelihood estimator for \(S\)  as follows: let
\(\mathcal {H}\)  be a finite dimensional approximation space for the KR rearrangement, i.e., let
\(\mathcal {H}\)  be a cone
of monotone triangular maps \(U:\mathbb {R}^n \rightarrow \mathbb {R}^n\)  that can be
described with finitely many parameters.
For each \(U\)  in \(\mathcal {H}\)  consider the density given by pulling back \(\eta \)  by \(U\) , defined as
\(U^\sharp \, \eta (U^{-1})_\sharp \, \eta \) 
and given explicitly by
\( U^\sharp \, \eta (z) =\eta (U(z))\,\det \nabla U(z), \) 
